Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#17984875 | C2 | semidirect |
| 3. C2×#17984821 | C2 | semidirect |
| 4. #22581117 | C2 | semidirect |
| 5. #22581111 | C2 | semidirect |
| 6. #22581106 | C2 | semidirect |
| 7. #22580955 | C2 | semidirect |
| 8. #407×C139 | C2 | semidirect |
| 15. C22×Dic278 | C22 | semidirect |
| 20. C2×Dic556 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 25. #17984821 | C22 | semidirect |
| 26. C2×C4⋊Dic139 | C22 | semidirect |
| 29. #17984767 | C22 | semidirect |
| 30. #17984764 | C22 | semidirect |
| 32. C2×M16×C139 | C22 | semidirect |
| 34. C22⋊C8×C139 | C22 | semidirect |
| 126. C22×C139 | #137 | semidirect |
| 146. C139 | #3007 | semidirect |
| 155. #407 | D139 | semidirect |
| 170. C2×M16 | C2×D139 | semidirect |
| 181. C22⋊C8 | C2×D139 | semidirect |
| 277. C22 | #17984875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555785 | 2 |
| C2×#17984875 | 2 |
| C2×#17984821 | 2 |
| #22581117 | 2 |
| #22581111 | 2 |
| #22581106 | 2 |
| #22580955 | 2 |
| #407×C139 | 2 |
| #3007 | 139 |